Licentiate seminar

Co-rotational shell element for elasto-plastic, quasi-static problems

Defendant Main Advisor Extra Advisor Date
Aleksandar Filipovski Anders Eriksson 2002-06-07


Evaluation committee


The work presented in this thesis deals with formulation of a co-rotational flat triangular element for the nonlinear analysis of shell structures. The element is based on the natural finite element formulation. It has three nodes with six degrees of freedom at each node. The membrane stiffness was formulated using a third order interpolation scheme which enabled evaluation of the drilling stiffness from the higher-order terms of the strain energy. \----------------------------------------------------------.... Two different formulations for the local co-rotated coordinate system proposed by Crisfield and Moita, [1] , and Rankin, [2], invariant with the respect to ordering of the node numbers, were exploited and compared. The property of energy orthogonality was enforced in the formulation, but numerical advantages of this enforcement were not observed during the tests on the benchmarks. \------------------.... An elasto-plastic constitutive model was introduced. Deformations were considered small. The shear strains and higher-order terms of the plane strain were considered elastic. A von Mises yielding hypothesis with an isotropic hardening was used to describe elasto-plastic behaviour of the material. Local internal forces and tangent stiffness matrices were computed by numerical integration throughout the thickness of the element. \----------------------------------------------------------------------------------.... The efficiency of proposed element is demonstrated by means of several numerical examples that include both geometrical and material nonlinearities. All of the numerical results presented show good accuracy and high computational efficiency of derived element even though the discretizations were performed with relatively coarse meshes. \-------------------------------------------------------------------------------.... Comparing the results from the tests to results referenced in the literature, leads to the conclusion that the co-rotational shell element presented in this thesis can efficiently be used for solving elasto-plastic, quasi-static problems. \----------------------------------------------------------.... \------------------------------------------------------...................... Keywords: elasto-plasticity, shell element, co-rotational method, natural finite element formulation, free formulation, FEM, structural analysis, path-following. \------ [1] Crisfield, M. A. and G.F. Moita,A unified co-rotational framework for solids, shells and beams, International journal of solids and structures, 1996, vol 33, pg 2969-2992. \--------------------------------------------.................. ................. ...................................... [2] C.C. Rankin, On choice of best possible corotational element frame , Modeling and simulation based engineering, Tech. Science Press, Forsyth, GA.,1998, vol.1, Edt. S. N. Atluri and P. E. O`Donoghue}, pgs. 772-777